Identification of filtered white noises

Albert Benassi, Serge Cohen, Jacques Istas and Stéphane Jaffard

Stochastic Processes and their Applications, 1998, vol. 75, issue 1, 31-49

Abstract: In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener integral, associated with the fractional Brownian motion, is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then, the identification of the first terms of this expansion is used to solve some filtering problems. Furthermore, rates of convergence of the estimators are then given.

Keywords: Gaussian; processes; Identification (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (12)

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